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71.
Udo Simon 《Results in Mathematics》2003,43(3-4):343-358
On an analytic Riemannian manifold (M,g), several authors have studied the Taylor expansion for the volume of geodesic balls under the exponential mapping. In the foregoing paper [1] we studied a more general structure (M,D,g), where D is a torsion-free and Ricci-symmetric connection. We calculated the Taylor expansion up to order (n+4) for the volume of what we called a generalized geodesic ball under the exponential mapping in case that all metric notions are Riemannian, while the exponential mapping is induced from the connection D. For the structure $(M,D,{\cal G})$ the coefficients of the Taylor expansion are much more complicated than in the Riemannian case. It is one of the main objectives of the present paper to study centroaffine hypersurfaces in Euclidean space, their geometric invariants which appear in the very complicated coefficient of order (n+4), and their behaviour under polarization (inversion at the unit sphere). Our results complement applications in the foregoing paper [1], where mainly the coefficients up to order (n+2) and geometric consequences have been studied. 相似文献
72.
This review is a survey of the many scientific applications of ultrasonic broadbandspectrometry (absorption and velocity measurements with coherent sound waves)in liquids and liquid systems, covering, at present, a frequency range from nearly10 kHz to 10 GHz. Ultrasonic spectrometry has proved to be an almost universalresearch tool in many laboratories, one that is useful for investigation of variouschemical, biochemical, and physicochemical systems. Sound waves traversingliquids induce periodic perturbations in pressure and temperature, which can shiftequilibria, resulting in characteristic sound absorption and velocity dispersionspectra. An analysis of such spectra yields valuable information about thermodynamic and kinetic parameters of the particular system that is often difficult toobtain by other methods. Since such periodic perturbations imposed on the systemare incremental in nearly all cases, the system can be studied under equilibriumconditions. All nonlinear effects (heating, nonconstant fluid compressibility, andothers) are negligible, permitting, for instance, the application of linearized rateequations. In this review, various examples of measured broadband spectra arepresented. Related elementary processes are discussed. Among these are ionicand molecular reactions, including mechanisms of association and complexation,proton transfer, solvation, isomerization, interconversion, side-group rotation,hydrogen-bonding, as well as stacking processes and micelle formation. Specialattention will be given to the extensive research on chemical relaxation.Fundamental early and recent publications are cited and discussed. Many referencesare included with particular emphasis on less well known research and publicationsfrom countries of the former USSR. This review aims at a demonstration of thewidespread applications of modern ultrasonic techniques in many fields ofliquid-state research. 相似文献
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J. Dorenbosch F. Udo J. V. Allaby U. Amaldi G. Barbiellini M. Baubillier F. Bergsma A. Capone W. Flegel F. Grancagnolo M. Jonker L. Lanceri M. Metcalf C. Nieuwenhuis J. Panman R. Plunkett C. Santoni K. Winter I. Abt F. W. Büsser H. Daumann P. D. Gall T. Hebbeker F. Niebergall P. Stähelin P. Gorbunov E. Grigoriev V. Kaftanov V. Khovansky A. Rosanov A. Baroncelli L. Barone B. Borgia C. Bosio M. Diemoz U. Dore F. Ferroni E. Longo L. Luminari P. Monacelli S. Morganti F. de Notaristefani L. Tortora V. Valente CHARM Collaboration 《Zeitschrift fur Physik C Particles and Fields》1989,41(4):567-589
A determination of sin2 θ w based on measurements of elastic scattering of muon-neutrinos and muon-anti-neutrinos on atomic electrons is described. These purely leptonic processes were studied using the CHARM calorimeter exposed to neutrino and antineutrino wide-band beams at the CERN super proton synchrotron. A total of 83±16 neutrino-electron and 112±21 antineutrino-electron events have been detected. From the measurement of the ratio of muon-neutrino and muon-antineutrino cross-sections a value of sin2 θ w =0.211±0.037 was obtained. 相似文献
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Seifert U 《Physical review letters》2011,106(2):020601
We consider nanosized artificial or biological machines working in steady state enforced by imposing nonequilibrium concentrations of solutes or by applying external forces, torques, or electric fields. For unicyclic and strongly coupled multicyclic machines, efficiency at maximum power is not bounded by the linear response value 1/2. For strong driving, it can even approach the thermodynamic limit 1. Quite generally, such machines fall into three different classes characterized, respectively, as "strong and efficient," "strong and inefficient," and "balanced." For weakly coupled multicyclic machines, efficiency at maximum power has lost any universality even in the linear response regime. 相似文献